## anonymous 4 years ago Find the values of the constants m and b, for which y=mx + b is a solution to this equation y'=1/2x + y - 1

You need to find values of $$m \text{ and }b$$ that satisfy the equation $m=\frac{1}{2}x+mx+b-1 \implies x(\frac{1}{2}+m)+b-1=m$ Now, equate coefficients, you get the system: $\frac{1}{2}+m=0 \implies m=-\frac{1}{2}$ $b-1=m \implies b=m+1=\frac{1}{2}.$ So, $$m=-\frac{1}{2}$$ and $$b=\frac{1}{2}$$.